Left handed materials using magnetic composites

ABSTRACT

A left-handed composite material which includes a mixture of a ferromagnetic material and a dielectric material. The direction of magnetization of the ferromagnetic material, and its volume fraction are controlled such that the composite material exhibits negative permeability in a frequency region near the ferromagnetic resonance frequency, and low eddy current losses. Furthermore, the handedness of the material may be locally tuned to be alternately converted into a right-handed material or a left-handed material by application of an external magnetic field, electric field, or mechanical stress. Such materials are easy to make and can be easily scaled up for industrial use.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. provisional application Ser.No. 60/361,910 filed on Feb. 28, 2002 which is incorporated herein byreference.

GOVERNMENT INTEREST

The U.S. Government has rights in this invention pursuant to ContractNos. ONRN00014-97-1-0300 and DAAD19-01-2-0001 between the Department ofDefense (Army Research Laboratory and the Office of Naval Research) andthe University of Delaware.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to left handed materials (LHM). Moreparticularly, the invention relates to left-handed material compositesand a process for making such composites. Such find use in theproduction of magnetic media and devices. Such media and devices cangenerate, detect, amplify, transmit, reflect, steer or otherwise controlelectromagnetic radiation for a variety of purposes. Such media may bechanged or modulated by an externally applied magnetic field, electricfield, or mechanical stress.

2. Description of the Related Art

According to conventional electrodynamics, the response of a material toelectric and magnetic fields is characterized by two fundamentalquantities, the permittivity ε and the permeability μ. The permittivityrelates the electric displacement field {right arrow over (D)} to theelectric field {right arrow over (E)} through {right arrow over(D)}=ε{right arrow over (E)}, and the permeability ε relates themagnetic field {right arrow over (B)} and {right arrow over (H)} by{right arrow over (B)}=μ{right arrow over (H)}.

Without taking losses into account and treating ε and μ as real numbers,according to Maxwell's equations, electromagnetic waves can propagatethrough a material only if the index of refraction n, given by(εμ)^(1/2), is real. It should be noted that dissipation will addimaginary components to ε and μ and cause losses, but for a qualitativepicture, one can ignore losses and treat ε and μ as real numbers. Also,ε and μ are second-rank tensors, but they reduce to scalars forisotropic materials.

In a medium with ε and μ both positive, the index of refraction is realand electromagnetic waves can propagate. Conventional transparentmaterials are examples of such kind of media. In a medium where one of εand μ is negative but the other is positive, the index of refraction isimaginary and electromagnetic waves cannot propagate. Examples of suchmedia include metals and Earth's ionosphere. Metals and the ionospherehave free electrons that have a natural frequency, the plasma frequency,which is on the order of 10 MHz in the ionosphere and falls at or abovevisible frequencies for most metals. At frequencies above the plasmafrequency, ε is positive and electromagnetic waves are transmitted. Forlower frequencies, ε becomes negative and the index of refraction isimaginary and consequently electromagnetic waves cannot propagatethrough. In fact, the electromagnetic response of metals in the visibleand near ultraviolet regions is dominated by the negative epsilonconcept.

Although conventional transparent materials have both positive ε andpositive μ, theoretically a medium wherein ε and μ are both negative theindex of refraction would also be positive, and electromagnetic wavescould also propagate through them. Moreover, the propagation of wavesthrough such a media should give rise to several peculiar properties.This was first pointed out by V. G. Veselago, Sov. Phys. Usp. 10, 509(1968), when no material with simultaneously negative ε and μ was known.For example, the cross product of {right arrow over (E)} and {rightarrow over (H)} for a plane wave in regular media gives the direction ofboth propagation and energy flow, and the electric field {right arrowover (E)}, the magnetic field {right arrow over (H)}, and the wavevector {right arrow over (k)} form a right-handed triplet of vectors. Incontrast, in a medium with ε and μ both negative, {right arrow over(E)}×{right arrow over (H)} for a plane wave still gives the directionof energy flow, but the wave itself, that is, the phase velocity,propagates in the opposite direction, i.e., wave vector {right arrowover (k)} lies in the opposite direction of {right arrow over(E)}×{right arrow over (H)} for propagating waves. In this case,electric field {right arrow over (E)}, magnetic field {right arrow over(H)}, and wave vector {right arrow over (k)} form a left-handed tripletof vectors. Such a medium is therefore termed a “left-handed” medium.

When an electromagnetic wave travels in a normal medium having bothpositive permittivity and permeability, the direction of electric field{right arrow over (E)}, magnetic field {right arrow over (H)}, and wavevector k satisfy the right-hand rule, i.e., {right arrow over(E)}×{right arrow over (H)} lies along the direction of k. Hence, thesematerials are termed right-handed. In contrast, a material whichsatisfies the opposite of the right-hand rule is termed left-handed. Ina left-handed material (LHM), however, {right arrow over (E)}×{rightarrow over (H)} lies along the direction of −k, i.e., the wave vector isin the opposite direction of the energy flow.

Left-handed materials demonstrate many unusual physical properties whichdiffer from those that govern the behavior of normal materials. Thereare a number of dramatically different propagation characteristicsstemming from a simultaneous change of the signs of ε and μ, includingreversal of both the Doppler shift and the Cerenkov radiation, anomalousrefraction, and even reversal of radiation pressure to radiationtension. However, although these counterintuitive properties followdirectly from Maxwell's equations, which still hold in these unusualmaterials, such left-handed materials have never been found in nature.Such media would be useful for various applications, such as in the areaof radiation-material interactions. Recently, progress has been achievedin preparing a ‘left-handed’ material artificially. Following thesuggestion of Pendry, et al Phys. Rev. Lett 76, 4773 (1996), Smith, etal Phys. Rev. Lett. 67, 3578 (2000) reported that a medium made up of anarray of conducting nonmagnetic split ring resonators and continuousthin wires can have both an effective negative permittivity ε andnegative permeability μ for electromagnetic waves propagating in somespecial direction and special polarization at microwave frequencies.However, the materials used in this proposed process suffer from variousdisadvantages, such as being difficult to make, particularly for scaleup fabrication. U.S. patent application publication U.S. 2001/0038325 A1describes other left handed composite media, however, such require anperiodically arranged, ordered array of conducting elements such aswires, which together with a medium, form a negative permeability,negative permittivity composite.

It would be desirable to formulate a left-handed material which is easyto make, especially on an industrial scale, and which can be locallytuned. The present invention provides a solution to these problems. Ithas now been found that by incorporating metallic magnetic nanoparticlesinto an appropriate insulating material, and by controlling thedirection of magnetization of the metallic magnetic components and theirvolume fraction, it is possible to prepare a composite medium of loweddy current loss, which is left-handed for electromagnetic wavespropagating in a special direction, and which has polarization in afrequency region near the ferromagnetic resonance frequency. Suchmaterials are advantageous because they are easy to make and can beeasily scaled up for industrial use. More importantly, the damping lossis very small. Furthermore, the handedness of the material may belocally tuned to be alternately converted into a right-handed materialor a left-handed material by application of an external magnetic fieldor mechanical stress.

The formation of the inventive left-handed composite materials ispossible because the permittivity of metallic particles is negative atfrequencies less than the plasma frequency, while the effectivepermeability of ferromagnetic materials for right circularly polarized(RCP) electromagnetic waves propagating parallel to the magnetizationdirection of the composite can be negative at frequency in the vicinityof the ferromagnetic resonance frequency ω₀, which is usually in thefrequency region of microwaves. Thus, by preparing a composite medium inwhich one component is both metallic and ferromagnetic and othercomponent insulating, and controlling the directions of magnetization ofmetallic magnetic particles and their volume fraction, it is possible toachieve a left-handed composite medium of low eddy current losses forelectromagnetic waves propagating in a special direction andpolarization.

SUMMARY OF THE INVENTION

The invention provides a left handed composite material which comprisesa substantially uniform mixture comprising a ferromagnetic material anda dielectric material, wherein the ferromagnetic material is present inthe composite material at a volume fraction below the conductivepercolation threshold of the composite; and wherein the compositematerial is at least partially transparent to electromagnetic radiation.

The invention also provides a method for forming a left handed compositematerial which comprises combining a ferromagnetic material and adielectric material to form a substantially uniform composite material;wherein the ferromagnetic material is present in the composite materialat a volume fraction below the conductive percolation threshold of thecomposite; and wherein the composite material is at least partiallytransparent to electromagnetic radiation.

The invention further provides an article which comprises a left handedcomposite material comprising a substantially uniform mixture comprisinga ferromagnetic material and a dielectric material, wherein theferromagnetic material is present in the composite material at a volumefraction below the conductive percolation threshold of the composite;and wherein the composite material is at least partially transparent toelectromagnetic radiation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(a) shows a graph of the frequency dependence of the real part ofthe effective permeability μ⁽⁺⁾ of magnetic grains for positivecircularly polarized plane waves.

FIG. 1(b) shows a graph of the corresponding frequency dependences ofthe effective wave number k and the effective damping coefficient β in acomposite consisting of metallic magnetic grains and dielectric grains.

FIG. 1(c) shows a graph of the corresponding frequency dependences ofthe effective wave number k and the effective damping coefficient β in acomposite consisting of metallic magnetic grains and dielectric grains.

FIG. 2(a) shows a graph of the frequency dependence of the effectivepermeability μ⁽⁻⁾ of magnetic grains.

FIG. 2(b) shows a graph of the frequency dependencies of the effectivewave number k.

FIG. 3 shows scanning electron micrographs (a)-(h) of Ni particulateloaded films.

FIG. 4 shows the amplitude (top) and phase (bottom) of the transmissionspectra in external magnetic field for Ni₂₀PS₈₀ with Ni particles ofabout 2 μm in size, embedded in a polystyrene matrix. All data arenormalized with respect to the amplitude and phase in zero field.

FIG. 5 shows the amplitude (top) and phase (bottom) of the transmissionspectra in external magnetic field for (FeNi)₃₀PS₇₀ with FeNi particlesof average diameter of 100 nm embedded in a polystyrene matrix. All dataare normalized with respect to the amplitude and phase in zero field.

FIG. 6 shows a transmission electron micrograph of (NiFe)₃₀PS₇₀ with 30vol. % of FeNi particles of average diameter of 100 nm embedded inpolystyrene matrix.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A left handed composite material is formed according to the invention.The left handed composite material comprises a substantially uniformmixture comprising a ferromagnetic material and a dielectric material.

Suitable ferromagnetic materials nonexclusively include iron, cobalt,nickel, ferrites, and alloys and combinations thereof. Most preferably,the ferromagnetic material comprises Fe, Ni, Co, FeNi, FeCo, FeCoNi,YIG, and/or SmCo alloys. The ferromagnetic material is preferablypresent in the composite material at a volume fraction below theconductive percolation threshold of the composite. This is because abovethe conductive percolation threshold, the composite material wouldbecome non-transparent. The ferromagnetic material is preferably presentin the composite material at an amount of from about 5% to about 45% byvolume of the composite material, more preferably from about 15% toabout 40% by volume of the composite material, and most preferably fromabout 25% to about 35% by volume of the composite material.

The ferromagnetic material may be present in any suitable shape whichwould allow for a substantially uniform mixture of the ferromagneticmaterial throughout the dielectric material. The ferromagnetic materialis preferably present in the form of particles, wires, rods, or plates.Preferably, the average ferromagnetic material particle size is fromabout 10 μm or less, more preferably from about 0.005 μm to about 1 μm,and most preferably from about 0.005 μm to about 0.5 μm. It is preferredthat the ferromagnetic particles have a particle size variation which isabout 20% or less compared to their average particle size.

Suitable dielectric materials nonexclusively include SiO₂, Al₂O₃, ZrO,TiO₂, Ta₂O₅ oxides, nitrides, organic and inorganic polymers, andcombinations thereof. Preferably, the dielectric material comprises amaterial which may be polyolefins, styrenics, polyamides, polyimides,polystyrene, polycarbonates, polyurethanes, acrylonitriles, acrylics,alkoxysilane polymers, silsesquioxane polymers, siloxane polymers,poly(arylene ether), a fluorinated poly(arylene ether),polytetrafluoroethylene (PTFE), and combinations thereof.

The composite material is preferably formed by combining theferromagnetic material and the dielectric material in a suitable mannerto thereby form a substantially uniform composite material. Suchcombining may be conducted by any conventional means such as by shearmixing, extrusion, blending, mechanical milling, ball milling,sputtering, vacuum deposition, chemical vapor deposition,electrochemical deposition, electroless deposition, chemical synthesis,sol gel fabrication, or self assembling. Extrusion is most preferred forproducing large quantity composites. High vacuum sputtering is morepreferred method for fabricating thin film samples. In one embodiment,the dielectric material is mixed with ferromagnetic material particlesand molded into a shaped article. In another embodiment, the dielectricmaterial is formed into dielectric templates with pores, and theferromagnetic material is filled inside the pores. In still anotherembodiment, the dielectric and ferromagnetic materials are mixed andthen hot-pressed into films. In still another embodiment, the dielectricand ferromagnetic materials are mixed on to a substrate from streams ofdielectric and ferromagnetic particle fluxes in vacuum.

The resulting composite material is at least partially transparent toelectromagnetic radiation. Preferably, the composite material ispreferably at least partially transparent to electromagnetic radiationin a frequency range of from about 10 MHz to about 10 THz. In apreferred embodiment, the composite material is preferably at leastpartially transparent to microwave radiation.

The following calculations based on the effective medium theory serve toillustrate the invention more clearly. A metallic magnetic granularcomposite is formed which includes of two types of spherical particles,one type of particles comprises metallic ferromagnetic grains of radiusR₁, and the other type comprises non-magnetic dielectric (insulating)grains of radius R₂. Each grain is substantially homogeneous. Thedirections of magnetization of all metallic magnetic grains are assumedto be in the same direction. In length scales larger than the grainsizes, the composite can be considered as a homogeneous magnetic system.The permittivity and permeability of non-magnetic dielectric grains areboth scalars, and will be denoted as ε₁ and μ₁. The permittivity ofmetallic magnetic grains will be denoted as ε₂ and will be taken to havea Drude form ε₂=1−ω_(p) ²/ω(ω+i/τ) where ω_(p) is the plasma frequencyof the metal and τ is a relaxation time. Such a form of ε isrepresentative of a variety of metal composites. The permeability ofmetallic magnetic grains are second-rank tensors and will be denoted as{circumflex over (μ)}₂, which can be derived from the Landau-Lifschitzequations. Assuming that the directions of magnetization of all magneticgrains are in the direction of the z-axis, {circumflex over (μ)}₂ willhave the following form: $\begin{matrix}{{\hat{\mu}}_{2} = {\begin{bmatrix}\mu_{a} & {{- i}\quad\mu^{\prime}} & 0 \\{i\quad\mu^{\prime}} & \mu_{a} & 0 \\0 & 0 & 1\end{bmatrix}\quad{where}}} & (1) \\{{\mu_{a} = {1 + \frac{\omega_{m}\left( {\omega_{0} + {{\mathbb{i}}\quad\alpha\quad\omega}} \right)}{\left( {\omega_{0} + {{\mathbb{i}}\quad\alpha\quad\omega}} \right)^{2} - \omega^{2}}}},} & \left( 20 \right. \\{{\mu^{\prime} = {- \frac{\omega_{m}\omega}{\left( {\omega_{0} + {{\mathbb{i}}\quad\alpha\quad\omega}} \right)^{2} - \omega^{2}}}},} & (3)\end{matrix}$ω₀=γ{right arrow over (H)}₀ is the ferromagnetic resonance frequency, H₀is the effective magnetic field in magnetic particles and may be a sumof the external magnetic field, the effective anisotropy field and thedemagnetization field; ω_(m)=γ{right arrow over (M)}₀, where γ is thegyromagnetic ratio, M₀ is the saturation magnetization of magneticparticles; α is the magnetic damping coefficient; ω is the frequency ofincident electromagnetic waves. Only incident electromagnetic wavespropagating in the direction of the magnetization are considered. Thegrain sizes are much smaller compared with the characteristic wavelengthλ, and consequently, electromagnetic waves in the composite can betreated as propagating in a homogeneous magnetic system. According toMaxwell's equations, electromagnetic waves propagating in the directionof magnetization in a homogeneous magnetic material is either right orleft circularly polarized (RCP or LCP). If the composite can truly betreated as a homogeneous magnetic system in the case of grain sizes muchsmaller than the characteristic wavelength, electric and magnetic fieldsin the composite should also be either right (superscript +) or left(superscript −) circularly polarized and can be expressed as:{right arrow over (E)}({right arrow over (r)},t)={right arrow over (E)}₀ ^((±)) e ^(ikz-βz-iωr)  (4){right arrow over (H)}({right arrow over (r)},t)={right arrow over (H)}₀ ^((±)) e ^(ikz-βz-iωr)  (4)where {right arrow over (E)}₀ ^((±))={circumflex over (x)}∓iŷ, {rightarrow over (H)}₀ ^((±))={circumflex over (x)}∓iŷ, k=Real[k_(eff)] is theeffective wave number, β=Im[k_(eff)] is the effective dampingcoefficient caused by the eddy current, k_(eff)=k+iβ is the effectivepropagation constant. In Equations (4)-(5) the signs of k and β can bothbe positive or negative depending on the directions of the wave vectorand the energy flow. Assume that the direction of energy flow is in thepositive direction of the z axis, i.e., β>0 in Equations (4)-(5), butthe sign of k still can be positive or negative. In this case, if k>0,the phase velocity and energy flow are in the same directions, and fromMaxwell's equation, the electric and magnetic field {right arrow over(E)} and {right arrow over (H)} and the wave vector {right arrow over(k)} will form a right-handed triplet of vectors. This is the usual casefor right-handed materials. In contrast, if k<0, the phase velocity andenergy flow are in opposite directions, and {right arrow over (E)},{right arrow over (H)} and {right arrow over (k)} will form aleft-handed triplet of vectors. This is the case for left-handedmaterials. Thus, for incident waves of a given frequency ω, it can bedetermined whether wave propagations in the composite is right-handed orleft-handed through the relative sign changes of k and β. Next, theeffective propagation constant k_(eff)=k+iβ shall be determined by meansof the effective medium approximation. If the composite is a homogeneousmagnetic system in the case of grain sizes much smaller than thecharacteristic wavelength, then for waves (positive or negativecircularly polarized) propagating through the composite in the directionof magnetization, their propagations are described by an effectivepermittivity ε_(eff) and an effective permeability μ_(eff) which satisfythe following relations: $\begin{matrix}{{\int{{\overset{\rightarrow}{D}\left( {\overset{\rightarrow}{r},\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{\quad z}}}{\mathbb{d}\overset{\rightarrow}{r}}}} = {ɛ_{eff}{\int{{\overset{\rightarrow}{E}\left( {\overset{\rightarrow}{r},\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{\quad z}}}{\mathbb{d}\overset{\rightarrow}{r}}}}}} & (6) \\{{\int{{\overset{\rightarrow}{B}\left( {\overset{\rightarrow}{r},\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{\quad z}}}{\mathbb{d}\overset{\rightarrow}{r}}}} = {\mu_{eff}{\int{{\overset{\rightarrow}{h}\left( {\overset{\rightarrow}{r},\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{\quad z}}}{\mathbb{d}\overset{\rightarrow}{r}}}}}} & (7)\end{matrix}$where k_(eff) and ω are related by k_(eff)=ω[ε_(eff)μ_(eff)]^(1/2).Although these relations are simple and in principle exact, it is verydifficult to calculate the integrals in them because the fields in thecomposite are spatially varying in a random way. Various types ofapproximations must therefore be used. The simplest approximation is theeffective medium approximation. In this approximation, the fields ineach grain are calculated as if the grain were embedded in an effectivemedium of dielectric constant ε_(eff) and magnetic permeability μ_(eff).Consider, for example, the ith grain. Under the embedding assumption,the electric and magnetic fields incident on the grain are the form ofEquations (4)-(5). $\begin{matrix}{{{\overset{\rightarrow}{E}}_{inc} = {{\overset{\rightarrow}{E}}_{0}^{( \pm )}\quad{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{- {iwt}}}}}},} & (8) \\{{{\overset{\rightarrow}{h}}_{inc} = {{\overset{\rightarrow}{h}}_{0}^{( \pm )}\quad{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{- {iwt}}}}}},} & (9)\end{matrix}$where {right arrow over (E)}₀ ^((±))={circumflex over (x)}∓iŷ and {rightarrow over (h)}₀ ^((±))={circumflex over (x)}∓iŷ, corresponding to theright (+) or left (−) circularly polarized waves. If the fields insidethe grain can be found, then the inside fields can be used to calculatethe integral over the grain volume. $\begin{matrix}{{{{\overset{\rightarrow}{I}}_{i} = {\int_{v_{i}}\quad{{{\overset{\rightarrow}{E}}_{i}\left( {\overset{\rightarrow}{r},\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{\quad z}}}{\mathbb{d}\overset{\rightarrow}{r}}}}},}\quad} & (10) \\{{{{\overset{\rightarrow}{J}}_{i} = {\int_{v_{i}}\quad{{{\overset{\rightarrow}{h}}_{i}\left( {\overset{\rightarrow}{r},\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad k_{{eff}^{\quad z}}}{\mathbb{d}\overset{\rightarrow}{r}}}}},}\quad} & (11)\end{matrix}$which is required to find the integral in Equations (6)-(7). For theright or left circularly polarized incident waves described by Esq.(8)-(9), the integral {right arrow over (I)}_(i), and {right arrow over(J)}_(i), can be written as:{right arrow over (I)} _(i)=({circumflex over (x)}+iŷ)I _(i),  (12){right arrow over (J)} _(i)=({circumflex over (x)}+iŷ)J _(i),  (13)where I_(i) and J_(i) are scalars. If I_(i) and J_(i) can be found, thenfrom Equations (6)-(7), the effective permittivity ε_(eff) and effectivepermeability μ_(eff) can be calculated by: $\begin{matrix}{{ɛ_{eff} = \frac{{f_{1}ɛ_{1}I_{1}} + {f_{2}ɛ_{2}I_{2}}}{{f_{1}I_{1}} + {f_{2}I_{2}}}},} & (14) \\{{\mu_{eff} = \frac{{f_{1}\mu_{1}J_{1}} + {f_{2}\mu_{2}^{( \pm )}J_{2}}}{{f_{1}J_{2}} + {f_{2}J_{2}}}},} & (15)\end{matrix}$where f₁ and f₂ are the volume fractions of the two types of grains, μ₁is the permeability of non-magnetic dielectric grains, μ₂ ⁽⁺⁾=μ_(α)−μ′and μ⁽⁻⁾=μ_(α)+μ′ (see Equations 1-3) are the effective permeability ofmagnetic grains for right and left circularly polarized wavesrespectively. For calculating I_(i) and J_(i), one can expand interiorand exterior fields in a multipole series and matching the boundaryconditions. After the coefficients of the multipole expansion ofinterior and exterior fields are obtained by matching the boundaryconditions, I_(i) and J_(i) can be found and subsequently be substitutedinto Equations (14)-(15). Such is a standard method in the art. In thefinal results, Equations (14)-(15) reduce to one self-consistentequation: $\begin{matrix}{{{\sum\limits_{{i = 1},2}^{\quad}{{fi}{\sum\limits_{i = 1}^{\infty}{\left( {{2l} + 1} \right)\left\lbrack {\frac{{k_{eff}{\psi_{l}^{\prime}\left( {k_{i}R_{i}} \right)}{\psi_{l}\left( {k_{eff}R_{i}} \right)}} - {k_{i}{\psi_{l}\left( {k_{i}R_{i}} \right)}{\psi_{l}^{\prime}\left( {k_{eff}R_{i}} \right)}}}{{k_{eff}{\psi_{l}^{\prime}\left( {k_{i}R_{i}} \right)}{_{l}\left( {k_{eff}R_{i}} \right)}} - {k_{i}{\psi_{l}\left( {k_{i}R_{i}} \right)}{_{l}^{\prime}\left( {k_{eff}R_{i}} \right)}}} + \frac{{k_{i}{\psi_{l}^{\prime}\left( {k_{i}R_{i}} \right)}{\psi_{l}\left( {k_{eff}R_{i}} \right)}} - {k_{eff}{\psi_{l}\left( {k_{i}R_{i}} \right)}{\psi_{l}^{\prime}\left( {k_{eff}R_{i}} \right)}}}{{k_{i}{\psi_{l}^{\prime}\left( {k_{i}R_{i}} \right)}{\varsigma_{l}\left( {k_{eff}R_{i}} \right)}} - {k_{eff}{\psi_{l}\left( {k_{i}R_{i}} \right)}{_{l}^{\prime}\left( {k_{eff}R_{i}} \right)}}}} \right\rbrack}}}} = 0},} & (16)\end{matrix}$where R_(i) is the radius of the ith type of grains, andk ₁=ω[ε₁μ₁]^(1/2),  (17)k ₂=ω[ε₂μ₂ ^((±))]^(1/2),  (18)ψ_(l)(x)=xj _(l)(x),  (19)

_(l)(x)=xh _(l) ⁽¹⁾(x),  (20)j_(l)(x) and h_(l)(x) are the usual spherical Bessel and Hankelfunctions. Equation (16) is used to determine the effective product of(εμ)_(eff), or equivalently k_(eff), but not a single ε_(eff) andμ_(eff). It can be used to describe the change of the phase of a planewave across a slab of the composite, but it does not precisely describewave propagations across a slab of the composite. This is due to thefact that no attempt is made to rigorously solve the boundary-valueproblem for a slab of composite by matching the fields inside the slaband external fields outside the slab at the boundary. In fact, it iscommon in various types of effective medium theories that for ω≠0 theelectromagnetic properties of a composite cannot in general be specifiedby a single ε_(eff) and μ_(eff). Since it can be determined whether wavepropagations through the composite is left-handed or right-handed by thecalculation of the effective propagation constant k_(eff), Equation (16)is sufficient.

The numerical results for a metal volume fraction f₂ of 0.3 obtainedfrom Equation (16) are summarized in FIG. 1-FIG. 2. FIG. 1(a) shows thefrequency dependence of the real part of the effective permeability μ⁽⁺⁾of magnetic grains for right circularly polarized plane waves, FIGS.1(b) and (c) show the corresponding frequency dependences of theeffective wave number k and the effective damping coefficient β in acomposite consisting of metallic magnetic grains and dielectric grains.The plasma frequency ω_(p) is usually in the visible or ultravioletfrequency region and the ferromagnetic resonance frequency ω₀ is usuallyin the microwave frequency region. For simplicity, hereafter we will setω_(o)/ω_(p)=10⁻⁵. The other parameters are: ω_(m)/ω₀=4.0, ω_(p)R/c=0.2,f₂=0.3, α is shown in the figures. From Equations (1)-(3), one canconclude that if the magnetic damping coefficient α is zero, Re[μ⁽⁺⁾]will be negative in the whole frequency region of ω>ω₀ (the magneticresonance frequency). From FIG. 1(a), it can be concluded that if α isnonzero but small enough, there can still be a frequency region near ω₀in which Re[μ⁽⁺⁾] is negative. In this case, if the amplitude of thenegative μ⁽⁺⁾ is large enough, k will be negative in this frequencyregion as was shown in FIG. 1(b), and hence the phase velocity andenergy flow will be in the opposite directions in this frequency region,and {right arrow over (E)}, {right arrow over (H)} and {right arrow over(k)} will form a left-handed triplet of vectors, i.e., the compositewill be left-handed in this frequency region for positive circularlypolarized plane waves. But if α is not small enough, Re[μ⁽⁺⁾] will bepositive in the whole frequency region, or though Re[μ⁽⁺⁾] is negativein a frequency region near ω₀, the amplitude of the negative Re[μ⁽⁺⁾] isnot large enough, in this case k will be positive in the whole frequencyregion, as was shown in FIG. 1(b). In this case, the composite isright-handed for positive circularly polarized waves in the wholefrequency region. The calculations also show that if the radius ofmetallic grains are small enough and the volume fraction of metalcomponents is smaller than the threshold value of the insulator-metaltransition, which is approximately {fraction (1/3)} in this model, thelosses caused by eddy current are very small and the composite isessentially an insulator. This is shown in FIG. 1(c), in which thedamping coefficient β is very small compared with the amplitude of thewave number k, i.e., the eddy current losses are very small in the casesshown in FIG. 1. If the volume fraction of metal components is largerthan the threshold value, the composite will be essentially a metal, andthe damping coefficient β will be much larger than the amplitude of wavenumber k (not shown in the figure).

FIG. 2(a) shows the frequency dependence of the real part of theeffective permeability μ⁽⁻⁾ of magnetic grains for left circularlypolarized waves, and FIG. 2(b) shows the corresponding frequencydependence of the effective wave number k in a composite consisting ofthe metallic magnetic grains and dielectric grains. Thus, for leftcircularly polarized waves, Re[μ⁽⁻⁾] is positive in the whole frequencyregion no matter how small α is, and correspondingly, k is positive inthe whole frequency region, i.e., the composite is right-handed in thewhole frequency region for left circularly polarized waves no matter howsmall α is.

The left-handed materials of the present invention exhibit the followingproperties:

-   -   (1) reversed Doppler effect—microwave radiation or light shift        to lower frequencies as a source approaches and to higher        frequency as it recedes;    -   (2) reversed Cerenkov effects—light emitted in the backward        direction (forward direction in a right-handed material) when a        charged particle passes though a medium; and    -   (3) reversed Snell's law—light that enters an LHM from a normal        material will undergo refraction, but opposite to that usually        observed.

The left-handed composite material of the invention may be formed into ashaped article. Such may be done by any conventional method such asmolding, extrusion molding, or the like.

In a preferred embodiment, the composite material may be alternatelyconverted into either right-handed composite material or a left-handedcomposite material by the application of a magnetic field or mechanicalstress.

Typical transmission patterns (amplitude and phase) of left handedcomposites in the external magnetic field are shown in FIG. 4 and FIG.5. The value of amplitude (top panels) and phase (bottom panels) arenormalized to the amplitude and phase, respectively, in zero field.

The left-handed materials of the invention can have many uses andapplications, such as electromagnetic wave (EM) signature management,phase shifters, phase array antennas, solid state antennas, filters,circulators, isolators, resonators, variable attenuators, modulators,and switches. Such left-handed materials are particularly useful for theformation of communication devices and elements. Left-handed materialscan also be used to make lenses such as perfect lenses, or lenses thatdo not have a diffraction limit.

The following non-limiting examples serve to illustrate the invention.It will be appreciated that variations in proportions and alternativesin elements of the components of the invention will be apparent to thoseskilled in the art and are within the scope of the present invention.

EXAMPLE 1

Fabrication of Co Nanoparticles:

-   -   1. Dissolve 17.5 g Co(OH)₂ into 350 ml ethylene glycol (EG) so        that the concentration of [Co²⁺] is around 0.2 M;    -   2. Slowly heat the solution with mechanic or magnetic stirring        to the boiling point of EG to distill off water and other small        molecules;    -   3. Weight 1˜10 mg K₂PtCl₄ and dissolve them into a few mL EG,        then inject the solution into above system so that the        concentration of K₂PtCl₄ is 0.05˜1 mM. This will generate many        tiny Pt clusters serving as nucleating center;    -   4. Continue heating the mixture and maintain refluxing for        several hours (3-5 hrs) before cooling down the mixture to RT.

5. The precipitation is separated from the solution by using a magnet orcentrifugator. The precipitates are first washed in de-ionized water for3 to 4 times, then in alcohol and acetone for several times, and finallydried at about 50° C. in argon atmosphere. The obtained Co nanoparticleshave sizes between 30 nm to 100 nm, saturation magnetization between120, to 160 emu/g, and coercive field Hc between 200 to 300 Oe.

EXAMPLE 2

Fabrication of CoNi Particles:

-   -   1. Dissolve 4.5 g Co(OH)₂ and 4.5 g NiCl₂ into 75 ml ethylene        glycol (EG);    -   2. Dissolve 6 g NaOH into 75 mL EG;    -   3. Mix above two solutions well by vigorous stirring;    -   4. Slowly heat the mixture to boiling and maintain refluxing for        3-5 hrs before cooling down the mixture to room temperature.    -   5. The precipitation is separated from the solution by using a        magnet or centrifugator. The precipitates are first washed in        de-ionized water for 3 to 4 times, then in alcohol and acetone        for several times, and finally dried at about 50° C. in argon        atmosphere. The obtained CoNi nanoparticles have size around 1        μm, saturation magnetization between 110 to 150 emu/g, and        coercive field Hc between 100 to 300 Oe.

EXAMPLE 3

Fabrication of Co Nanoparticles:

Pour 200 ml mineral oil into the bottom of a reaction beaker; 5.384 g ofCoCl₂.6H₂O is first dispersed and partly dissolved into 200 ml ethanoland then added on the top of the oil. (Oleic acid can be added to reducethe agglomeration of magnetic particles). 1.712 g of NaBH₄ is dissolvedinto 200 ml ethanol and then add into above solution in a drop-likemanner by using a dropping funnel. A magnet under the reaction beaker isused to attract the formed magnetic particles into the oil phase. Afterthe reaction is completed, with the help of the magnet, the supernatantsolution and the oil are dismissed. The slurries are first washed byalcohol and acetone for several times to remove the residual oil, thenfollowed by rinsing in de-ionized water for several times to thoroughlyremove NaCl formed during the reaction, and finally washed by acetoneagain to remove water. The formed Co nanoparticles are either kept inmineral oil or a vacuum desiccator. The obtained Co nanoparticles haveof 4.7 nm with standard deviation 1.6 nm, saturation magnetizationbetween 60 to 80 emu/g, and coercive field Hc between 50 to 200 Oe.

EXAMPLE 4

Fabrication of FeNi Particles:

Pour 200 ml mineral oil into the bottom of a reaction beaker; 17.753 gof FeCl₂.4H₂O and 21.2277 g of NiCl₂.6H₂O are first dispersed and partlydissolved into 400 ml ethanol and then added on the top of the oil.(Oleic acid can be added to reduce the agglomeration of magneticparticles). 13.516 g of NaBH₄ is dissolved into 300 ml ethanol and thenadd into above solution in a drop-like manner by using a droppingfunnel. A magnet under the reaction beaker is used to attract the formedmagnetic particles into the oil phase. After the reaction is completed,with the help of the magnet, the supernatant solution and the oil aredismissed. The slurries are first washed by alcohol and acetone forseveral times to remove the residual oil, then followed by rinsing inde-ionized water for several times to thoroughly remove NaCl formedduring the reaction, and finally washed by acetone again to removewater. The formed FeNi nanoparticles are either kept in mineral oil or avacuum desiccator.

EXAMPLE 5

Fabrication of FeCo Particles:

Pour 200 ml mineral oil into the bottom of a reaction beaker; 17.321 gof FeCl₂.4H₂O and 20.729 g of CoCl₂.6H₂O are first dispersed and partlydissolved into 500 ml ethanol and then added on the top of the oil.(Oleic acid can be added to reduce the agglomeration of magneticparticles). 13.183 g of NaBH₄ is dissolved into 300 ml ethanol and thenadd into above solution in a drop-like manner by using a droppingfunnel. A magnet under the reaction beaker is used to attract the formedmagnetic particles into the oil phase. After the reaction is completed,with the help of the magnet, the supernatant solution and the oil aredismissed. The slurries are first washed by alcohol and acetone forseveral times to remove the residual oil, then followed by rinsing inde-ionized water for several times to thoroughly remove NaCl formedduring the reaction, and finally washed by acetone again to removewater. The formed FeCo nanoparticles are either kept in mineral oil or avacuum desiccator.

EXAMPLE 6

Fabrication of M_(x)(Polystyrene)_(100-x) Composites (M: Co, FeNi, FeCo,CoNi, Ni, Fe, and Ni, x is the Volume Concentration in the Range of0<x<50)

The particles prepared above are dispersed in polystyrene toluenesolution and sonicated for 20-30 minutes. The amount will be determinedaccording to the value of x. The dispersion is then put into an oven andheated to about 80° C. to allow the toluene evaporate. The raw materialswill be cut into small pieces and fed into DACA twin-screw extruder. Theextruder temperature is set to about 170° C. The materials are mixedbetween two screws along the channel of the microcompounder for about10-20 minutes. After the extrusion, magnetic particles can behomogeneously dispersed into the polymer matrix and the materials can behot pressed in any desirable shape. FIG. 3 shows SEM micrographs (a)-(h)of the Ni particulate loaded composite of each particle size and volumefraction. A transmission electron micrograph for FeNi loaded compositeis shown in FIG. 6.

EXAMPLE 7

Fabrication of (Fe₁₉N₈₁)₂₅(SiO₂)₇₅ Films:

A magnetron sputtering target of (Fe₁₉Ni₈₁)₂₅(SiO₂)₇₅ was used, wheresubscripts outside the parentheses represent volume concentration. Thecomposite film of a nominal composition (Fe₁₉Ni₈₁)₂₅(SiO₂)₇₅ wasfabricated at 4 mT Ar pressure using magnetron sputtering technique.

EXAMPLE 8

Fabrication of Anodic Alumina Template (AAT) with Random Pores:

A 0.1 mm thick aluminum foil of 99.5 purity is first heated at 500° C.for 5 hours to reduce the internal stress and defects. The foil is thenplaced in a 1M NaOH solution for 1 minute to remove surface aluminumoxide. The foil is then anodized for 3 hours with a DC power supply in asolution of 0.4M H₂SO₄ at 0° C., under a potential of 25V. The AAT soobtained is about 20 μm in thickness, pore separation is about 60 nm.Different separations can be obtained with different potentials. Thepores are widened in a solution of 6 wt % H₃PO₄ at 30° C. for 20minutes, and the pore diameter is about 25 nm. Different pore diameterscan be obtained by controlling the time.

EXAMPLE 9

Fabrication of Anodic Alumina Template (AAT) with Ordered Pores:

A 1 mm thick aluminum foil of purity 99.999 is first heated at 500° C.for 24 hours to reduce the internal stress and defects. The foil is thenplaced in a 1M NaOH solution for 3 minutes to remove surface aluminumoxide. The foil is then anodized for 10 hours in a solution of 0.4MH₂SO₄ at 0° C., with an external potential of 25V. The foil issubsequently placed in a solution of 6 wt % H₃PO₄ and 1.8 wt % H₂CrO₄ at60° C. for 10 hours to etch away the alumina made during the previousstep. The foil is again anodized for 10 hours in a solution of 0.4MH₂SO₄ at 0° C. with an external potential of 25V. The AAT so obtained isabout 20 μm in thickness, pore separation is about 60 nm. Differentseparation can be obtained with different potentials. The pores arewidened in a solution of 6 wt % H₃PO₄ at 30° C. for 20 minutes, and thepore diameter is about 25 nm. Different pore diameters can be obtainedby controlling the time.

EXAMPLE 10

Filling the Magnetic Metals (Fe, Ni Co, FeNi, FeCo) Inside the Pore:

An anodic alumina template (AAT) is formed according to Example 2 or 3.After the fabrication of the AAT, the remaining aluminum works as acathode. Fe, Ni, Co, FeNi or FeCo are electrodeposited into thenanopores by galvanic method from corresponding sulfate solutions. Theelectrolytes for Fe, Ni or Co are 0.1M FeSO₄, 0.1M NiSO₄, or 0.1M CoSO₄respectively. 0.1M H₃BO₃ are added to the above solutions to adjust thePH values. The current density is about 10 mA/cm². For FeCo, we useFeSO₄.7H₂O 57 g/L, CoSO₄.7H₂O 79 g/L, H₃BO₃ 30 g/L, and Saccharin 2-2.7g/L. The current density is about 15 mA/cm², and an Fe_(0.45)CO_(0.55)alloy nanowire array is obtained. For FeNi case, one applies FeSO₄.7H₂O6 g/L, NiSO₄.7H₂O 140 g/L, H₃BO₃ 30 g/L, and Fe₁₄Ni₈₆ is obtained.

EXAMPLE 11

A left handed composite material of the invention is formed according toExamples 1-10. The high frequency magnetic permeability of thesematerials is measured using a HP network analyzer with fixturesincluding stripline, coaxial cable, microstripline, co-planar waveguide,permeameter, and resonant cavity of 500 MHz base frequencies. Negativepermeability above the ferromagnetic resonance is observed in FeNifilms. FeNi particles do not show a negative permeability without a DCbias magnetic field. With an external DC bias magnetic field, thenegative permeability of FeNi particles can be seen. When FeNi is mixedwith various polymer matrixes, it exhibits negative permeability in FeNibased composites. Furthermore, microwave reflection and transmissionmeasurement are performed.

While the present invention has been particularly shown and describedwith reference to preferred embodiments, it will be readily appreciatedby those of ordinary skill in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe invention. It is intended that the claims be interpreted to coverthe disclosed embodiment, those alternatives which have been discussedabove and all equivalents thereto.

1. A left handed composite material which comprises a substantiallyuniform mixture comprising a ferromagnetic material and a dielectricmaterial, wherein the ferromagnetic material is present in the compositematerial at a volume fraction below the conductive percolation thresholdof the composite; and wherein the composite material is at leastpartially transparent to electromagnetic radiation.
 2. The left handedcomposite material of claim 1 wherein said ferromagnetic materialcomprises ferromagnetic particles, wires, rods, or plates.
 3. The lefthanded composite material of claim 1 wherein said ferromagnetic materialcomprises ferromagnetic particles.
 4. The left handed composite materialof claim 3 wherein the ferromagnetic particles have an average particlesize of about 10 μm or less.
 5. The left handed composite material ofclaim 3, wherein the ferromagnetic particles have a particle sizevariation which is about 20% or less compared to their average particlesize.
 6. The left handed composite material of claim 1, wherein theferromagnetic material is present in the composite material at an amountof from about 5% to about 40% by volume of the composite material. 7.The left handed composite material of claim 1, wherein the ferromagneticmaterial is selected from the group consisting of iron, cobalt, nickel,ferrites, and alloys and combinations thereof.
 8. The left handedcomposite material of claim 1, wherein the ferromagnetic materialcomprises Fe, Ni, Co, FeNi, FeCo, FeNiCo, SmCo or combinations thereof.9. The left handed composite material of claim 1, wherein the dielectricmaterial comprises a material selected from the group consisting ofSiO₂, Al₂O₃, Ta₂O₅, oxides, nitrides, organic and inorganic polymers,and combinations thereof.
 10. The left handed composite material ofclaim 1, wherein the dielectric material comprises a material selectedfrom the group consisting of polyolefins, styrenics, polyamides,polyimides, polystyrene, polycarbonates, polyurethanes, acrylonitriles,acrylics, alkoxysilane polymers, silsesquioxane polymers, siloxanepolymers, poly(arylene ether), a fluorinated poly(arylene ether),polytetrafluoroethylene, and combinations thereof.
 11. The left handedcomposite material of claim 1, wherein the dielectric material comprisesSiO₂.
 12. The left handed composite material of claim 1 wherein thecomposite is at least partially transparent to electromagnetic radiationin a frequency range of from about 10 MHz to about 10 THz.
 13. The lefthanded composite material of claim 1 wherein the composite is at leastpartially transparent to microwave radiation.
 14. The left handedcomposite material of claim 1, wherein the composite material is capableof being alternately converted into either a right-handed material or aleft-handed material by application of an external magnetic field ormechanical stress.
 15. A method for forming a left handed compositematerial which comprises combining a ferromagnetic material and adielectric material to form a substantially uniform composite material;wherein the ferromagnetic material is present in the composite materialat a volume fraction below the conductive percolation threshold of thecomposite; and wherein the composite material is at least partiallytransparent to electromagnetic radiation.
 16. The method of claim 15,wherein the combining is conducted by shear mixing, extrusion, blending,mechanical milling, ball milling, sputtering, vacuum deposition,chemical vapor deposition, electrochemical deposition, electrolessdeposition, chemical synthesis, sol gel fabrication, or self assembling.17. The method of claim 15 further comprising the subsequent step offorming the composite material into a shaped article.
 18. The method ofclaim 17 wherein the shaped article is formed by molding or extrusionmolding.
 19. The method of claim 15, further comprising the step ofalternately converting the composite material into either right-handedcomposite material or a left-handed composite material by theapplication of a magnetic field or mechanical stress.
 20. The method ofclaim 15 wherein said ferromagnetic material comprises ferromagneticparticles, wires, rods, or plates.
 21. The method of claim 15 whereinsaid ferromagnetic material comprises ferromagnetic particles.
 22. Themethod of claim 21 wherein the ferromagnetic particles have an averageparticle size of about 10 μm or less.
 23. The method of claim 21,wherein the ferromagnetic particles have a particle size variation whichis about 20% or less compared to their average particle size.
 24. Themethod of claim 15, wherein the ferromagnetic material is present in thecomposite material at an amount of from about 5% to about 40% by volumeof the composite material.
 25. The method of claim 15, wherein theferromagnetic material is selected from the group consisting of iron,cobalt, nickel, ferrites, and alloys and combinations thereof.
 26. Themethod of claim 15, wherein the ferromagnetic material comprises Fe, Ni,Co, FeNi, FeCo, FeNiCo, and/or SmCo.
 27. The method of claim 15, whereinthe dielectric material comprises a material selected from the groupconsisting of SiO₂, Al₂O₃, Ta₂O₅, oxides, nitrides, organic andinorganic polymers, and combinations thereof.
 28. The method of claim15, wherein the dielectric material comprises a material selected fromthe group consisting of polyolefins, styrenics, polyamides, polystyrene,polyimides, polycarbonates, polyurethanes, acrylonitriles, acrylics,alkoxysilane polymers, silsesquioxane polymers, siloxane polymers,poly(arylene ether), a fluorinated poly(arylene ether),polytetrafluoroethylene, and combinations thereof.
 29. The method ofclaim 15, wherein the dielectric material comprises SiO₂.
 30. The methodof claim 15 wherein the composite is at least partially transparent toelectromagnetic radiation in a frequency range of from about 10 MHz toabout 10 THz.
 31. The method of claim 15 wherein the composite is atleast partially transparent to microwave radiation.
 32. An article whichcomprises a left handed composite material comprising a substantiallyuniform mixture comprising a ferromagnetic material and a dielectricmaterial, wherein the ferromagnetic material is present in the compositematerial at a volume fraction below the conductive percolation thresholdof the composite; and wherein the composite material is at leastpartially transparent to electromagnetic radiation.